Abstract
As environmental problems are increasingly challenging and sustainable development win support among the people, the energy-efficient hybrid flow-shop scheduling problem (HFSP), as a scheduling problem with great application value, has been widely concerned. However, most existing research has focused on deterministic cases and uncertainty is rarely considered in energy-efficient HFSP (EHFSP), especially with various machine speed constraints. Uncertainty is often caused by some uncontrollable factors, such as human factors and ignoring uncertainty will greatly reduce the application value of the problem solutions. In this study, an energy-efficient fuzzy HFSP (EFHFSP) at a variable machine speed is considered and the existing non-dominated sorting genetic algorithm-II (NSGA-II) is extended to minimize fuzzy make-span and total fuzzy energy consumption simultaneously. The computation of total fuzzy energy consumption is given and reverse learning is proposed to produce the initial population. ENSGA-II adopts an effective genetic operator and its parameters (Pc and Pm) are adjustive. A novel strategy based on history information is also used to produce high-quality solutions. Extensive experiments are conducted to test the performance of ENSGA-II. ENSGA-II can provide promising results for EFHFSP.
•A multi-objective mathematical model for energy-efficient fuzzy hybrid slow-shop scheduling with various machine speed is formulated.•In order to solve the problem of the subtraction of triangular fuzzy number not satisfying the closure, a repairing measure is proposed.•The operands of NSGA-II are changed from crisp numbers to triangular fuzzy numbers.•The main loop of NSGA-II is improved to enhance the efficiency of extended NSGA-II.